I had fallen and cut myself in a dirty gutter. X-ray, examination by ER physician, tetanus shot, prescription for antibiotics.
Same thing in London about 15 years ago when my mother fell and injured her head. The resident who treated her just couldn't be bothered with the paperwork.
The difference was that we were in the UK at the nadir of the Thatcher effect. My local friend drove us at top speed to the nearest hosptial in working-class northeast London. There, we spent 5 hours in the ER waiting room after being triaged. The nurse had no ice to give us for the huge lump on my mother's forehead, and I had no change, so I had to bum money from the people in the waiting room -- mainly obviously low-income people and immigrants and a couple of rather seriously mentally ill individuals -- to buy cold Coke from the machine to hold to her head. There was blood on the floor when we entered and when we left, and blood got added to the reception desk as we were there.
When the resident told us to go home and put ice on the injury, I looked at the nurse who had had no ice, and said "Ice. What a novel idea." He said "Well that's what you get when you have a single-tier health system." I said "We have a single-tier health system at home. We also have ice."
The *fact* was that the UK had a TWO-tier health system, and that was the whole problem. As we waited in the ER, my local friend's partner was in a private room in a private hospital, because they had private insurance, choosing her meals from the room-service menu. The public tier of the system had been left to languish, as funding was increasingly withdrawn.
This is why we in Canada will fight tooth and nail to keep private health insurance out of our health system. Us and Cuba.

I doubt that you can expect to move to single public payer in the US overnight -- we didn't in Canada, remember; it took decades to get the public plan nationally after it started in one province, to get full health coverage rather than just hospital coverage, and eventually to get private insurers and co-pays to providers ("extra billing") out of the system.
But try not to give up on a strong public insurer component when you start on this path. Regulation of the private insurance market is a good and necessary step too, but I hope you get a foot on the public payer ladder soon.